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Another approach to characterizations of generalized triangle inequalities in normed spaces

Tamotsu Izumida, Ken-Ichi Mitani, Kichi-Suke Saito (2014)

Open Mathematics

In this paper, we consider a generalized triangle inequality of the following type: x 1 + + x n p x 1 p μ 1 + + x 2 p μ n f o r a l l x 1 , ... , x n X , where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].

Answer to a question by M. Feder about K(X,Y).

G. Emmanuele (1993)

Revista Matemática de la Universidad Complutense de Madrid

We show that a Banach space constructed by Bourgain-Delbaen in 1980 answers a question put by Feder in 1982 about spaces of compact operators.

Antiproximinal sets in the Banach space c ( X )

S. Cobzaş (1997)

Commentationes Mathematicae Universitatis Carolinae

If X is a Banach space then the Banach space c ( X ) of all X -valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C ( X ) V has a nearest point in V .

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